phpmyadmin can only import files up to 2Mb. How large is your file? if it is too big, just cut your file down to multiple files under that limit. thats what i do.
for example, if you have a few tables that are really large first i dump the structure and duplicate it on the new server. then i import as many tables i can fit into the 2Mb limit and break up any tables that are too large and dump them piece by piece. works for me.
I had to do this once. It was a pain and took some time, but I got it done eventually.
In phpmyadmin, go to import, and get the page where you can copy/paste SQL code in. Open your .sql file locally with Wordpad. Copy and paste the stuff in. No more than about 20 pages at a time (make sure you start at the beginning of a table and end at the end of a table, doesn't have to be the same table though).
I know it's a pain in the ***, but if you can't get anything else working, this may be your only bet.